0009.tex

\begin{exerciseStatement}


Explain how to find the general solution to the given ODE.

\[ 0 = {y'} - 6 \, {y} + {y''} + 62 \, \cos\left(5 \, t\right) + 10 \, \sin\left(5 \, t\right) \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {y} = k_{2} e^{\left(2 \, t\right)} + k_{1} e^{\left(-3 \, t\right)} + 2 \, \cos\left(5 \, t\right) \]
\end{exerciseAnswer}